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Reinforcement Learning (RL) has empowered Large Language Models (LLMs) with strong reasoning capabilities, but vanilla RL mainly focuses on generation capability improvement by training with only first-order rollout (generating multiple responses for a question), and we argue that this approach fails to fully exploit the potential of training data because of the neglect of critique capability training. To tackle this problem, we further introduce the concept of second-order rollout (generating multiple critiques for a response) and propose a unified framework for jointly training generation and critique capabilities. Extensive experiments across various models and datasets demonstrate that our approach can utilize training data more effectively than vanilla RL and achieve better performance under the same training data. Additionally, we uncover several insightful findings regarding second-order rollout and critique training, such as the importance of label balance in critique training and the noise problem of outcome-based rewards, which can be mitigated through sampling techniques. Our work offers a preliminary exploration of dynamic data augmentation and joint generation-critique training in RL, providing meaningful inspiration for the further advancement of RL training